First, $100,000 notes were never released to the public, they only circulated between banks.

Your perspective is kind of culturally biased. U.S. notes have always been of standard size regardless of denomination - so that's what you are used to. But many countries did (and still do) have denominations that varied in size, so citizens there came to expect high-value notes to be physically larger than small change. They would ask an American why our currency is so small.

First, $100,000 notes were never released to the public, they only circulated between banks.

Your perspective is kind of culturally biased. U.S. notes have always been of standard size regardless of denomination - so that's what you are used to. But many countries did (and still do) have denominations that varied in size, so citizens there came to expect high-value notes to be physically larger than small change. They would ask an American why our currency is so small.

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Now my question is, how would people carry around these enormous bills?

The Russian 100 and 500 ruble bills are forearm-sized. There’s no reasonable way anybody could carry this around, except in an A4 size folio or something.

Even smaller ones, like old Yugoslavian notes are way too big to fit in anything less than a straight up folio.

I think people routinely used coins in day to day market transactions.
Perhaps the bed sheet sized money was a way to store wealth, status symbol without really spending it, rather than keep it in a bank which may not have been insured then, and, perhaps that made it more difficult for counterfeiters?
It is a fair question.

The early European banknotes were basically documents about a contract. You would bring so and so much money to a bank (or other trusted "money dealer") and get an elaborate receipt, some even hand-written, about the amount. Later these documents were used just like the "real money" they represented. Note that on some banknotes you still find statements such as the BoE's "I promise to pay the bearer on demand ..."

Size matters. Would you value a piece of paper the size of a postage stamp? Would you value a half dimes as much as silver dollar? Sure, much of that is psychological but much of the value of paper money, anybody's paper money, is just that, psychological.

The Philippine peso devalued right around that time, I don't think it's worth that much.
"In the early 1990s, the peso devalued again to 28 per dollar. Due to the 1997 Asian financial crisis, the peso devalued from 29 per dollar in July 1997 to 46.50 in 1998 and about 50 in 2001."

So IDK if this is worth the same as the new peso after the devaluation.